QuestionShort Answer
6. a) Determine the slope of the line that passes through the point: $(-2,-3)$ and $(5,4)$ .

Studdy Solution

STEP 1

1. We are given two points on a line: $(-2, -3)$ and $(5, 4)$ .
2. We need to determine the slope of the line passing through these points.

STEP 2

1. Recall the formula for the slope of a line.
2. Substitute the given points into the slope formula.
3. Simplify the expression to find the slope.

STEP 3

Recall the formula for the slope of a line. The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by:
$m = \frac{y_2 - y_1}{x_2 - x_1}$

STEP 4

Substitute the given points $(-2, -3)$ and $(5, 4)$ into the slope formula. Here, $(x_1, y_1) = (-2, -3)$ and $(x_2, y_2) = (5, 4)$ .
$m = \frac{4 - (-3)}{5 - (-2)}$

STEP 5

Simplify the expression to find the slope.
First, simplify the numerator:
$4 - (-3) = 4 + 3 = 7$
Next, simplify the denominator:
$5 - (-2) = 5 + 2 = 7$
Thus, the slope $m$ is:
$m = \frac{7}{7} = 1$
The slope of the line is:
$\boxed{1}$

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