Question

The equation of the graphed line is 2x – 3y = 12.

A coordinate plane with a line passing through (0, negative 4) and (6, 0).
What is the x-intercept of the graph?

–4
–Negative StartFraction 3 Over 2 EndFraction
StartFraction 2 Over 3 EndFraction
6

Answer 1

Explanation:

The x-intercept of a graph is the point where the line crosses the x-axis, meaning the y-coordinate of that point is zero. To find the x-intercept, we need to determine the value of x when y is 0.

Given the line passing through (0, -4) and (6, 0), we can use the coordinates to calculate the slope of the line:

Slope (m) = (Change in y) / (Change in x)

Slope (m) = (0 - (-4)) / (6 - 0)

Slope (m) = 4 / 6

Slope (m) = 2 / 3

Now we have the slope (m) of the line. The equation of a line in point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line. Using the point (6, 0), we can write the equation as:

y - 0 = (2/3)(x - 6)

y = 2/3x - 4

Now, to find the x-intercept, we set y to 0:

0 = 2/3x - 4

2/3x = 4

x = (3/2) * 4

x = 6

So, the x-intercept of the graph is 6.