In the graph shown, identify the y–intercept & slope. Write the equation of this line in Slope-Intercept form.

$y=$\frac$23x+1$

$y=-$\frac$23x+1$

$y=-2x+1$

$y=x+2$

Verified step by step guidance

Identify the y-intercept of the line by locating the point where the line crosses the y-axis. In this graph, the line crosses the y-axis at y = 1.

Determine the slope of the line by selecting two points on the line. For example, choose the y-intercept (0, 1) and another point, such as (1, -1).

Calculate the slope using the formula: $ m = \frac{y_2 - y_1}{x_2 - x_1} $. Substitute the points (0, 1) and (1, -1) into the formula: $ m = \frac{-1 - 1}{1 - 0} = \frac{-2}{1} = -2 $.

Write the equation of the line in slope-intercept form, $ y = mx + b $, where m is the slope and b is the y-intercept. Substitute m = -2 and b = 1 into the equation: $ y = -2x + 1 $.

Verify the equation by checking that the line passes through the points used to calculate the slope. Substitute x = 0 and x = 1 into the equation $ y = -2x + 1 $ to ensure it yields the correct y-values (1 and -1, respectively).

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