Question

find the x- and y-intercepts of the graph of $-3x + y = 26$. state each answer as an integer or an improper fraction in simplest form.

answer attempt 1 out of 10

x-intercept: \boxed{ } y-intercept: \boxed{ }

Explanation:

Step1: Find x - intercept (set y = 0)

To find the x - intercept, we set \(y = 0\) in the equation \(-3x + y=26\). Substituting \(y = 0\) into the equation gives us \(-3x+0 = 26\), which simplifies to \(-3x=26\). Then we solve for \(x\) by dividing both sides of the equation by \(- 3\). So \(x=\frac{26}{-3}=-\frac{26}{3}\).

Step2: Find y - intercept (set x = 0)

To find the y - intercept, we set \(x = 0\) in the equation \(-3x + y = 26\). Substituting \(x = 0\) into the equation gives us \(-3(0)+y=26\), which simplifies to \(y = 26\).

Answer:

x - intercept: \(-\frac{26}{3}\)
y - intercept: \(26\)