Question

Identify the slope and y-intercept of the line −2x+5y=−30.

Answer 1

The slope of the line −2x+5y=−30 is 2/5, and the y-intercept is -6, with the slope indicating a moderate rate of ascent and the y-intercept showing where the line crosses the y-axis at (0, -6).

Step-by-step explanation:

To identify the slope and y-intercept of the line given by the equation −2x+5y=−30, we must first rewrite the equation in slope-intercept form, which is y = a + bx or y = mx + b (where m is the slope and b is the y-intercept). To do this, we solve for y:

5y = 2x - 30
y = (2/5)x - 6

Now, the equation is in the slope-intercept form (y = mx + b), where the coefficient of x is the slope and the constant term is the y-intercept. Therefore, the slope is 2/5, and the y-intercept is -6.

The slope of 2/5 indicates that for every increase of 5 units in x, y increases by 2 units, reflecting a moderate rate of ascent. The y-intercept of -6 tells us that the line crosses the y-axis at the point (0, -6).

Answer 2

slope = 2/5 , y-intercept = -30

Step-by-step explanation:

-2x + 5y = -30

5y = 2x - 30

y = 2/5x - 6

we know that the general form is:

y = (slope)*x + (y- intercept)

so, from our equation, we can say that...

slope = 2/5

y- intercept = -30