Math / Geometry

QuestionA straight line is shown on the coordinate grid below.

Studdy Solution

STEP 1

1. The line passes through the points $(-2, -3)$ and $(2, 3)$ .
2. We need to find the equation of the line.

STEP 2

1. Determine the slope of the line.
2. Use the point-slope form to find the equation of the line.
3. Simplify the equation to slope-intercept form.

STEP 3

Determine the slope of the line using the formula for slope:
$m = \frac{y_2 - y_1}{x_2 - x_1}$
Substitute the given points $(-2, -3)$ and $(2, 3)$ :
$m = \frac{3 - (-3)}{2 - (-2)}$ $= \frac{3 + 3}{2 + 2}$ $= \frac{6}{4}$ $= \frac{3}{2}$

STEP 4

Use the point-slope form of the equation of a line:
$y - y_1 = m(x - x_1)$
Substitute the slope $m = \frac{3}{2}$ and one of the points, say $(-2, -3)$ :
$y - (-3) = \frac{3}{2}(x - (-2))$ $y + 3 = \frac{3}{2}(x + 2)$

STEP 5

Simplify the equation to slope-intercept form $y = mx + b$ :
Distribute the slope:
$y + 3 = \frac{3}{2}x + \frac{3}{2} \times 2$ $y + 3 = \frac{3}{2}x + 3$
Subtract 3 from both sides to solve for $y$ :
$y = \frac{3}{2}x + 3 - 3$ $y = \frac{3}{2}x$
The equation of the line is:
$\boxed{y = \frac{3}{2}x}$

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