Linear Equations: y=mx+c Practice

Cards · 52

Identify the slope (m) and y-intercept (c) in y = 3x + 7.

m = 3, c = 7. In standard slope-intercept form y = mx + c, the coefficient of x is the slope (3) and the constant term is the y-intercept (7).

Identify the slope (m) and y-intercept (c) in y = -5x - 2.

m = -5, c = -2. Comparing with y = mx + c, the coefficient of x gives m = -5 and the constant term gives c = -2.

Identify the slope and y-intercept in y = 4 - 2x.

m = -2, c = 4. Rearrange the terms into y = mx + c format: y = -2x + 4. Thus slope m = -2 and y-intercept c = 4.

Identify the slope and y-intercept in y = x/2 + 3.

m = 1/2, c = 3. Rewrite x/2 as (1/2)x. In y = mx + c, the coefficient m is 1/2 and the constant c is 3.

Identify the slope and y-intercept in y = 8.

m = 0, c = 8. Rewrite as y = 0x + 8. A horizontal line has a slope of 0 and crosses the y-axis at (0, 8).

Identify the slope and y-intercept in y = -x.

m = -1, c = 0. Rewrite as y = -1x + 0. The slope is -1 and the line passes through the origin, so c = 0.

Find the slope of a line passing through (1, 2) and (3, 8).

m = 3. Use slope formula m = (y2 - y1) / (x2 - x1) = (8 - 2) / (3 - 1) = 6 / 2 = 3.

Find the slope of a line passing through (-2, 5) and (2, -3).

m = -2. Apply m = (y2 - y1) / (x2 - x1) = (-3 - 5) / (2 - (-2)) = -8 / 4 = -2.

Find the slope of a line passing through (4, 7) and (9, 7).

m = 0. Apply m = (7 - 7) / (9 - 4) = 0 / 5 = 0. Equal y-values indicate a horizontal line.

Find the slope of a line passing through (3, -1) and (3, 5).

Undefined slope. Using m = (5 - (-1)) / (3 - 3) gives 6 / 0. Division by zero means the line is vertical.

Find the slope of a line passing through (-1, -4) and (3, 8).

m = 3. Using formula m = (8 - (-4)) / (3 - (-1)) = 12 / 4 = 3.

Convert 2x + y = 6 into y = mx + c form.

y = -2x + 6. Subtract 2x from both sides to isolate y: y = -2x + 6.

Convert 4x - 2y = 10 into y = mx + c form.

y = 2x - 5. Subtract 4x: -2y = -4x + 10. Divide every term by -2: y = 2x - 5.

Convert 3x + 6y = 12 into y = mx + c form.

y = -1/2x + 2. Subtract 3x: 6y = -3x + 12. Divide everything by 6: y = (-3/6)x + (12/6) = -1/2x + 2.

Convert x - 3y + 9 = 0 into y = mx + c form.

y = 1/3x + 3. Add 3y to both sides: x + 9 = 3y. Divide each term by 3: y = 1/3x + 3.

Convert 5x + 2y - 8 = 0 into y = mx + c form.

y = -5/2x + 4. Isolate 2y: 2y = -5x + 8. Divide both sides by 2: y = -5/2x + 4.

Find the equation of a line with slope 4 and y-intercept -3.

y = 4x - 3. Substitute m = 4 and c = -3 directly into y = mx + c.

Find the equation of a line with slope -1/2 passing through (0, 5).

y = -1/2x + 5. The point (0, 5) gives c = 5 directly. Substitute m = -1/2 and c = 5 into y = mx + c.

Find the equation of a line with slope 2 passing through (1, 5).

y = 2x + 3. Use y = mx + c: substitute 5 = 2(1) + c, giving 5 = 2 + c, so c = 3. Thus, y = 2x + 3.

Find the equation of a line with slope -3 passing through (2, 1).

y = -3x + 7. Substitute into y = mx + c: 1 = -3(2) + c -> 1 = -6 + c -> c = 7. Thus, y = -3x + 7.

Find the equation of a line with slope 5 passing through (-1, -2).

y = 5x + 3. Substitute into y = mx + c: -2 = 5(-1) + c -> -2 = -5 + c -> c = 3. Thus, y = 5x + 3.

Find equation of line through (0, 2) and (4, 10).

y = 2x + 2. Slope m = (10 - 2) / (4 - 0) = 8 / 4 = 2. Since (0, 2) is on the y-axis, c = 2. Result: y = 2x + 2.

Find equation of line through (1, 3) and (3, 7).

y = 2x + 1. Slope m = (7 - 3)/(3 - 1) = 4/2 = 2. Solve for c: 3 = 2(1) + c, so c = 1. Equation is y = 2x + 1.

Find equation of line through (2, -1) and (6, 7).

y = 2x - 5. Slope m = (7 - (-1))/(6 - 2) = 8/4 = 2. Solve for c: -1 = 2(2) + c -> -1 = 4 + c -> c = -5. Equation: y = 2x - 5.

Find equation of line through (-2, 4) and (2, 0).

y = -x + 2. Slope m = (0 - 4)/(2 - (-2)) = -4/4 = -1. Solve for c: 0 = -1(2) + c -> c = 2. Equation: y = -x + 2.

Find the x-intercept of the line y = 3x - 9.

x = 3. Set y = 0: 0 = 3x - 9 -> 3x = 9 -> x = 3. The coordinate is (3, 0).

Find the x-intercept of the line y = -2x + 8.

x = 4. Set y = 0: 0 = -2x + 8 -> 2x = 8 -> x = 4. The coordinate is (4, 0).

Find the x-intercept of the line 4x + 3y = 12.

x = 3. Set y = 0: 4x + 3(0) = 12 -> 4x = 12 -> x = 3. The coordinate is (3, 0).

Find the y-intercept of the line 2x - 5y = 15.

y = -3. Set x = 0: 2(0) - 5y = 15 -> -5y = 15 -> y = -3. The coordinate is (0, -3).

What is the slope of any line parallel to y = 4x - 5?

m = 4. Parallel lines have identical slopes. The given line has m = 4, so any parallel line also has m = 4.

Find equation of line parallel to y = 3x + 1 passing through (0, -4).

y = 3x - 4. Parallel means m = 3. The point (0, -4) is on the y-axis, so c = -4. Result: y = 3x - 4.

Find equation of line parallel to y = -2x + 4 passing through (2, 3).

y = -2x + 7. Parallel slope m = -2. Find c using (2, 3): 3 = -2(2) + c -> 3 = -4 + c -> c = 7. Result: y = -2x + 7.

What is the slope of any line perpendicular to y = 2x + 3?

m = -1/2. Perpendicular slopes are negative reciprocals: m_perp = -1 / m = -1 / 2.

What is the slope of any line perpendicular to y = -3/4x + 2?

m = 4/3. Negative reciprocal of -3/4 is -1 / (-3/4) = 4/3.

Find equation of line perpendicular to y = 1/3x - 2 passing through (0, 1).

y = -3x + 1. Perpendicular slope m = -1 / (1/3) = -3. Point (0, 1) means c = 1. Result: y = -3x + 1.

Find equation of line perpendicular to y = 2x + 5 passing through (4, 1).

y = -1/2x + 3. Perpendicular slope is -1/2. Solve for c: 1 = (-1/2)(4) + c -> 1 = -2 + c -> c = 3. Result: y = -1/2x + 3.

Does the point (2, 7) lie on the line y = 3x + 1?

Yes. Substitute x = 2: y = 3(2) + 1 = 6 + 1 = 7. Since the calculated y matches 7, the point lies on the line.

Does the point (3, -2) lie on the line y = -2x + 5?

No. Substitute x = 3: y = -2(3) + 5 = -6 + 5 = -1. Because -1 does not equal -2, the point does not lie on the line.

Find the value of k if (k, 10) lies on y = 4x - 2.

k = 3. Substitute into equation: 10 = 4k - 2. Add 2: 12 = 4k. Divide by 4: k = 3.

Find the value of k if (2, k) lies on 3x + 2y = 16.

k = 5. Substitute x = 2 and y = k: 3(2) + 2k = 16 -> 6 + 2k = 16 -> 2k = 10 -> k = 5.

Find the intersection point of y = 2x + 1 and y = x + 4.

(3, 7). Set equal: 2x + 1 = x + 4 -> x = 3. Substitute x into either equation: y = 3 + 4 = 7.

Find the intersection point of y = -x + 6 and y = 2x - 3.

(3, 3). Set equal: -x + 6 = 2x - 3 -> 9 = 3x -> x = 3. Substitute x: y = -(3) + 6 = 3.

Find the intersection point of y = 3x - 5 and y = -2x + 10.

(3, 4). Set equal: 3x - 5 = -2x + 10 -> 5x = 15 -> x = 3. Substitute: y = 3(3) - 5 = 4.

What is the equation of the line passing through (5, 2) and (5, -4)?

x = 5. Both points share the x-coordinate 5. The line is vertical with undefined slope, written as x = 5.

What is the equation of the line passing through (-3, 4) and (2, 4)?

y = 4. Both points share the y-coordinate 4. The line is horizontal with slope 0, written as y = 4.

Find the slope of the line 3x - 4y = 8.

m = 3/4. Rearrange to y = mx + c: -4y = -3x + 8 -> y = (3/4)x - 2. The slope is the coefficient of x, which is 3/4.

Find the slope of the line 5x + 10y = 7.

m = -1/2. Rearrange: 10y = -5x + 7 -> y = (-5/10)x + 7/10 -> y = -1/2x + 7/10. The slope is -1/2.

Find the equation of a line with y-intercept -6 and x-intercept 2.

y = 3x - 6. Points are (0, -6) and (2, 0). Slope m = (0 - (-6)) / (2 - 0) = 6/2 = 3. With c = -6, equation is y = 3x - 6.

Find the midpoint between intercepts of line 2x + y = 8.

(2, 4). x-intercept (y=0) is (4, 0). y-intercept (x=0) is (0, 8). Midpoint = ((4+0)/2, (0+8)/2) = (2, 4).

Determine if y = 2x + 1 and 2x - y + 5 = 0 are parallel, perpendicular, or neither.

Parallel. Rearrange second line: y = 2x + 5. Both lines have m = 2 and different intercepts, so they are parallel.

Determine if y = 3x - 2 and x + 3y = 9 are parallel, perpendicular, or neither.

Perpendicular. Rearrange second line: 3y = -x + 9 -> y = -1/3x + 3. Since slopes are 3 and -1/3, their product is -1.

Find the distance between the parallel lines y = 2 and y = -3.

5 units. Both lines are horizontal. The vertical distance between y = 2 and y = -3 is |2 - (-3)| = 5.