Question

find the intercepts and graph the equation by plotting points.
$17x^2 + 25y = 425$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the intercept(s) is/are .
(type an ordered pair. use a comma to separate answers as needed.)

b. there are no intercepts.

use the graphing tool to graph the equation.

click to enlarge graph

Explanation:

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

Substitute $y=0$ into $17x^2 + 25y = 425$:
$$17x^2 = 425$$
$$x^2 = \frac{425}{17} = 25$$
$$x = \pm 5$$
So x-intercepts are $(-5, 0)$ and $(5, 0)$.

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

Substitute $x=0$ into $17x^2 + 25y = 425$:
$$25y = 425$$
$$y = \frac{425}{25} = 17$$
So y-intercept is $(0, 17)$.

Step3: List all intercepts

Combine the ordered pairs from steps 1 and 2.

Answer:

A. The intercept(s) is/are $(-5, 0), (5, 0), (0, 17)$

(For graphing: plot the intercepts, then solve for y to get $y = \frac{425 - 17x^2}{25} = 17 - \frac{17}{25}x^2$, calculate additional points like $(2, 17 - \frac{17}{25}(4)) = (2, 14.48)$ and $(-2, 14.48)$, then draw a downward-opening parabola through all points.)