Graph lines, use slope-intercept form, and find intercepts.
Free, timed SHSAT practice sets on graphing lines & slope-intercept form— every question includes a full worked explanation, and there's no account required.
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In \(y = mx + b\), \(m\) is the slope and \(b\) is the \(y\)-intercept (the value of \(y\) when \(x = 0\)).
Common traps: mixing up the two intercepts, giving \(m\) when the question asks for \(b\), and forgetting to divide the constant when you divide by the number in front of \(y\).
Solve for \(y\): \(-6y = -11 + 4x\), so \(y = \dfrac{4}{-6}x + \dfrac{-11}{-6}\), giving \(y = -2/3x + 11/6\). (Forgetting the minus sign when moving \(-4x\) gives \(y = 2/3x + 11/6\). Dividing only the \(x\)-term by \(-6\) gives \(y = -2/3x - 11\). Turning the slope fraction upside down gives \(y = -3/2x + 11/6\).)
Set \(y = 0\): \(0 = -8x + 2\), so \(x = \dfrac{-2}{-8} = 1/4\). (Forgetting the minus sign when moving the \(2\) gives \(-1/4\). Setting \(x = 0\) instead finds the \(y\)-intercept, \(2\). Multiplying by \(-8\) instead of dividing gives \(16\).)
Slope \(m = \dfrac{-5}{-2} = 5/2\). Using point \((-1, 8)\): \(b = y - mx = 8 - (5/2)(-1) = 21/2\). Equation: \(y = 5/2x + 21/2\). (Turning the slope fraction upside down gives \(y = 2/5x + 42/5\). Getting the sign of the slope wrong gives \(y = -5/2x + 11/2\). Finding the slope but never finding \(b\) gives \(y = 5/2x\).)