Question

the equation of a line is given below.
$7x - 5y = -35$
(a) find the x-intercept and the y-intercept.
$x$-intercept:
$y$-intercept:
(b) use the intercepts to graph the line.

Explanation:

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

Substitute $y=0$ into $7x-5y=-35$:
$7x - 5(0) = -35$
$7x = -35$
$x = \frac{-35}{7} = -5$

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

Substitute $x=0$ into $7x-5y=-35$:
$7(0) - 5y = -35$
$-5y = -35$
$y = \frac{-35}{-5} = 7$

Step3: Graph using intercepts

Plot the x-intercept point $(-5, 0)$ and y-intercept point $(0, 7)$, then draw a straight line through these two points.

Answer:

(a)
x-intercept: $-5$
y-intercept: $7$
(b)

1. Plot the point $(-5, 0)$ on the x-axis.
2. Plot the point $(0, 7)$ on the y-axis.
3. Draw a straight line connecting these two points to graph the line $7x-5y=-35$.