The graph of the line that contains the point (-6,1) and has a slope of 5 is plotted below
The graph passes through (-6, 1)
For a line passing through the point (x₁, y₁), with a slope of m, the equation is given as:
[tex]y-y_1 = m(x - x_1)[/tex]
Substitute x₁ = -6, y₁ = 1, and m = 5 into the equation [tex]y-y_1 = m(x - x_1)[/tex]
[tex]y - 1 = 5(x - (-6))\\\\[/tex]
Simplify the expression:
y - 1 = 5(x + 6)
y - 1 = 5x + 30
y = 5x + 30 + 1
y = 5x + 31
The equation y = 5x + 31 is of the form y = mx + c
where the slope, m = 5
the y-intercept, c = 31
Plot the graph with slope, m = 5, and y-intercept, c = 31 as shown below
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