Line ℓ passes through the points (2,2) and (4,10). What is the slope of line ℓ ? Choose 1 answer: (A) -4 (B) (1)/(4) (C) 4 (D) 5

Use Slope Formula: To find the slope of a line that passes through two points, we use the slope formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.Substitute Given Points: Substitute the given points into the slope formula. Let (2,2) be (x1, y1) and (4,10) be (x2, y2). So, m = (10 - 2) / (4 - 2).Calculate Differences: Calculate the difference in y-coordinates and x-coordinates. Difference in y-coordinates: 10 - 2 = 8. Difference in x-coordinates: 4 - 2 = 2.Divide Differences: Divide the difference in y-coordinates by the difference in x-coordinates to find the slope. m = 8 / 2.Perform Division: Perform the division to find the slope. m = 8 / 2 = 4.

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Math Problems

Algebra 1

Slopes of parallel and perpendicular lines

Full solution

Q. Line

\ell

passes through the points

(2,2)

and

(4,10)

. What is the slope of line

\ell

\newline

Choose

1

answer:

\newline

(A)

-4

\newline

(B)

\frac{1}{4}

\newline

(C)

4

\newline

(D)

5

Use Slope Formula: To find the slope of a line that passes through two points, we use the slope formula: slope $m$ = $\frac{y_2 - y_1}{x_2 - x_1}$ , where $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
Substitute Given Points: Substitute the given points into the slope formula. Let $(2,2)$ be $(x_1, y_1)$ and $(4,10)$ be $(x_2, y_2)$ . So, $m = \frac{10 - 2}{4 - 2}$ .
Calculate Differences: Calculate the difference in y-coordinates and x-coordinates. $\newline$ Difference in y-coordinates: $10 - 2 = 8$ . $\newline$ Difference in x-coordinates: $4 - 2 = 2$ .
Divide Differences: Divide the difference in $y$ -coordinates by the difference in $x$ -coordinates to find the slope. $m = \frac{8}{2}.$
Perform Division: Perform the division to find the slope. $\newline$ $m = \frac{8}{2} = 4$ .