Answer:
y = -3x + 7
Step-by-step explanation:
In order to determine the linear equation in slope-intercept form, y = mx + b, we must first determine its slope, and y-intercept.
Slope:
The slope (also referred to as the rate of change) is the measure of the steepness of a line. We can solve for the slope of the line using the following slope formula:
[tex]\displaystyle\mathsf{\textbf{Slope\:(m)} =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
We must choose two points from the graph.
Let (x₁, y₁) = (1, 4)
(x₂, y₂) = (0, 7)
Substitute these values into the slope formula:
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{y_2 - y_1}{x_2 - x_1}}[/tex]
[tex]\displaystyle\mathsf{Slope\:(m) =\:\frac{7-4}{0-1}\:=\frac{3}{-1}\:=\:-3}[/tex]
Hence, the slope of the line is -3.
Y-intercept:
Next, we must determine the y-intercept of the graph. The y-intercept is the point on the graph where it crosses the y-axis, with its coordinates occurring at point (0, b). The value of "b" is the y-intercept that we use in the slope-intercept form.
Observing the given graph, it shows that the line crosses the y-axis at point (0, 7). Therefore, the y-intercept, b = 7.
Linear Equation:
Now that we have our slope, m = -3, and y-intercept, b = 7, we can write the following linear equation in slope-intercept form:
y = -3x + 7
