A line representing the linear function f is graphed in the xy-plane. The line intersects … — SAT

A line representing the linear function $f$ is graphed in the $xy$ -plane. The line intersects the $y$ -axis at $(0, 3)$ and also passes through the point $(2, 11)$ . What is the slope of this line?

Answer: 4

Answer

The slope of the line is 4.

The slope

m

of a line passing through two points

(x_1, y_1)

and

(x_2, y_2)

is given by the formula

m = \frac{y_2 - y_1}{x_2 - x_1}

. Substituting the given points

(0, 3)

and

(2, 11)

into the formula gives

m = \frac{11 - 3}{2 - 0} = \frac{8}{2} = 4

Step-by-Step Solution

Identify two coordinates on the line from the given information.

The points are

(0, 3)

and

(2, 11)

To find the slope of a line, we need at least two points on that line.

Apply the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{11 - 3}{2 - 0}

The slope formula calculates the ratio of the vertical change (rise) to the horizontal change (run).

Perform the subtraction and division to find the slope value.

m = \frac{8}{2} = 4

Simplifying the fraction gives the final numerical slope.

Key Concept

Calculating the slope of a linear function given two points

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