QuestionUse the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through $(-3,-2)$ and $(2,3)$
What is the equation of the line in point-slope form? $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.) What is the equation of the line in slope-intercept form? $\square$ (Simplify your answer. Use integers or fractions for any numbers in the equation.)

Studdy Solution

STEP 1

1. We need to find the equation of a line passing through two given points.
2. The line equation should be expressed in both point-slope form and slope-intercept form.

STEP 2

1. Calculate the slope of the line using the two points.
2. Write the equation in point-slope form using one of the points.
3. Convert the point-slope form equation to slope-intercept form.

STEP 3

To find the slope $m$ of the line passing through the points $(-3, -2)$ and $(2, 3)$ , use the formula for the slope between two points: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute $(x_1, y_1) = (-3, -2)$ and $(x_2, y_2) = (2, 3)$ : $m = \frac{3 - (-2)}{2 - (-3)} = \frac{3 + 2}{2 + 3} = \frac{5}{5} = 1$

STEP 4

Using the point-slope form of the equation of a line, $y - y_1 = m(x - x_1)$ , and the point $(-3, -2)$ : $y - (-2) = 1(x - (-3))$ Simplify: $y + 2 = 1(x + 3)$

STEP 5

Convert the point-slope form equation $y + 2 = 1(x + 3)$ to slope-intercept form $y = mx + b$ . First, distribute the slope: $y + 2 = x + 3$ Subtract 2 from both sides to solve for $y$ : $y = x + 1$
The equation of the line in point-slope form is: $y + 2 = 1(x + 3)$
The equation of the line in slope-intercept form is: $y = x + 1$

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