Math  /  Algebra

Question16 Find the slope and yy-intercept from the following graph of a linear equation. (A) slope =4=4 and yy-intercept =3=3

Studdy Solution

STEP 1

1. The graph represents a linear equation.
2. The line passes through the points (0,3)(0, 3) and (1,7)(1, 7).
3. The slope-intercept form of a linear equation is y=mx+by = mx + b, where mm is the slope and bb is the yy-intercept.

STEP 2

1. Identify the points on the graph.
2. Calculate the slope of the line.
3. Determine the yy-intercept from the graph.
4. Verify the calculated slope and yy-intercept.

STEP 3

Identify the points through which the line passes. From the image description, the points are (0,3)(0, 3) and (1,7)(1, 7).

STEP 4

Calculate the slope mm using the formula for the slope between two points (x1,y1)(x_1, y_1) and (x2,y2)(x_2, y_2):
m=y2y1x2x1 m = \frac{y_2 - y_1}{x_2 - x_1}
Substitute the given points (0,3)(0, 3) and (1,7)(1, 7):
m=7310=41=4 m = \frac{7 - 3}{1 - 0} = \frac{4}{1} = 4

STEP 5

Determine the yy-intercept bb. The yy-intercept is the point where the line crosses the yy-axis. From the point (0,3)(0, 3), we see that the yy-intercept is 33.

STEP 6

Verify the calculated slope and yy-intercept by checking if they match the given options. The calculated slope is 44 and the yy-intercept is 33, which matches option (A).
The slope is 44 and the yy-intercept is 33.

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