Write the point-slope form of the given line that passes through the points (0, 3) and (4, 0). Identify (x1, y1) as the x-intercept of the line. Include your work in your final answer. Type your answer in the box provided to submit your solution.
Question
Write the point-slope form of the given line that passes through the points (0, 3) and (4, 0). Identify (x1, y1) as the x-intercept of the line. Include your work in your final answer. Type your answer in the box provided to submit your solution.
Solution
The point-slope form of a line is given by the formula:
y - y1 = m(x - x1)
where m is the slope of the line and (x1, y1) is a point on the line.
First, we need to find the slope of the line. The slope is given by the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points (0, 3) and (4, 0) into the formula, we get:
m = (0 - 3) / (4 - 0) = -3/4
Next, we identify (x1, y1) as the x-intercept of the line. The x-intercept is the point where the line crosses the x-axis, which is where y = 0. From the given points, we can see that the x-intercept is (4, 0).
So, substituting m = -3/4 and (x1, y1) = (4, 0) into the point-slope form, we get:
y - 0 = -3/4(x - 4)
Simplifying this, we get the point-slope form of the line:
y = -3/4x + 3
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