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A coordinate plane with a line passing through the points (negative 4, negative 5) and (1, negative 1).

Write an equation in standard form of the line that is graphed. Then find the x- and y-intercepts.

The equation of the line in standard form is
.

The x-intercept is
.

The y-intercept is
.

1 Answer

8 votes

Final answer:

The standard form of the line passing through (-4, -5) and (1, -1) is -4x + 5y = -9. The x-intercept is 9/4 or 2.25, and the y-intercept is -9/5 or -1.8.

Step-by-step explanation:

To find an equation of a line in standard form passing through two points, we need to start by calculating the slope of the line. The slope m is determined by the change in y divided by the change in x between two points (x1, y1) and (x2, y2).

In this case, we have the points (-4, -5) and (1, -1). So the slope m is calculated as:

m = (y2 - y1) / (x2 - x1)
m = (-1 - (-5)) / (1 - (-4))
m = (4) / (5)
m = 4/5

The slope is positive, so we know it's not a line with a negative slope. We can use the slope and one point to write the slope-intercept form of the line: y - y1 = m(x - x1). Using the point (-4, -5), we get:

y + 5 = (4/5)(x + 4)

To convert this to standard form (Ax + By = C), we clear the fractions and move all terms involving variables to the left side and constant terms to the right side of the equation:

5(y + 5) = 4(x + 4)
5y + 25 = 4x + 16
-4x + 5y = -9

The standard form of the line is -4x + 5y = -9. Now, to find the x-intercept, set y to 0 and solve for x:

-4x = -9
x = 9/4

The x-intercept is 9/4 or 2.25.

To find the y-intercept, set x to 0 and solve for y:

5y = -9
y = -9/5

The y-intercept is -9/5 or -1.8.

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