The graph of the line with slope -3 passing through the point (5,1) is attached.
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
What is the equation of a line?
The equation of a line is the representation of a line on a coordinate plane (x-y plane), which shows the relation between x and y, for every point on the particular line.
The standard form of a line is ax + by = c, where x and y are variables and a, b, and c are constants.
The slope-intercept form of a line is y = mx + b, where x and y are variables, m is the slope of the line, and b is the y-intercept of the line.
What is the one-point formula of a straight line?
The equation of a line passing through the point (x₁, y₁), having a slope m, is represented by the one-point formula: y - y₁ = m(x - x₁).
How do we solve the given question?
We are asked to graph a line with a slope = -3, passing through the point (5, 1).
We use the one-point formula to determine the equation of this line, with slope m = -3, (x₁, y₁) = (5, 1).
Substituting these values in the equation y - y₁ = m(x - x₁), we get
y - 1 = -3(x - 5)
or, y = -3x + 15 + 1
or, y = -3x + 16.
or, 3x + y = 16
The equation of the line in the slope-intercept form is y = -3x + 16.
The equation of the line in the standard form is 3x + y = 16.
To graph this line we plot the points (5, 1) (as it is given that it passes through this point) and (0, 16) (as the y-intercept is at 16, so the line passes through the point (0, 16)). We join these points by a line and extend this line on both sides to get the required line.
Learn more about the graphing of a line at
https://brainly.com/question/4025726
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