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Slope & Linear Equations — Practice Problems

Test your understanding of slope, linear equations, and the relationship between parallel and perpendicular lines. Each problem includes a full worked solution.

Quick Recap

The slope between two points is m=y2−y1x2−x1m = \frac{y_2 - y_1}{x_2 - x_1}. Parallel lines have equal slopes. Perpendicular lines have slopes that are negative reciprocals: m1⋅m2=−1m_1 \cdot m_2 = -1. The three main equation forms are slope-intercept (y=mx+by = mx + b), point-slope (y−y1=m(x−x1)y - y_1 = m(x - x_1)), and standard (Ax+By=CAx + By = C).

Practice Problems

1
Find the slope of the line through (2,5)(2, 5) and (6,13)(6, 13).
2
Write the equation of a line with slope 33 passing through (1,7)(1, 7) in slope-intercept form.
3
A line has equation y=−25x+3y = -\frac{2}{5}x + 3. What is the slope of a line perpendicular to it?
4
Are the lines y=4x−1y = 4x - 1 and y=4x+7y = 4x + 7 parallel, perpendicular, or neither?
5
Find the slope of the line 3x+6y=123x + 6y = 12.
6
Find the x-intercept and y-intercept of 2x−3y=122x - 3y = 12.
7
A line is perpendicular to y=34x−2y = \frac{3}{4}x - 2 and passes through (3,1)(3, 1). Write its equation.
8
The line through (−1,4)(-1, 4) and (3,k)(3, k) has slope −2-2. Find kk.
9
What is the slope of any horizontal line?
10
Line ℓ1\ell_1 has slope 27\frac{2}{7}. Line ℓ2\ell_2 passes through (0,0)(0,0) and (7,−2)(7, -2). Are they perpendicular?

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