Given the line below.
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 or use the upload option to submit your solution.
well the slope is -3/4, and the point slope is
y-k = m(x-h)
so plug in your numbers. It does not matter which point you choose for (h,k).
To write the point-slope form of the line passing through the points (0, 3) and (4, 0), we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of one of the points on the line, and m is the slope of the line.
First, let's find the slope (m) using the formula:
m = (y2 - y1) / (x2 - x1)
Given the points (0, 3) and (4, 0), we have:
(x1, y1) = (0, 3) and (x2, y2) = (4, 0)
Substituting these values into the slope formula, we get:
m = (0 - 3) / (4 - 0)
m = -3 / 4
Now that we have the slope (m), we can write the point-slope form using one of the given points. Let's use (0, 3) as (x1, y1):
y - 3 = (-3/4)(x - 0)
Simplifying this equation, we get:
y - 3 = (-3/4)x
This is the point-slope form of the given line passing through the points (0, 3) and (4, 0). The x-intercept occurs when y = 0, so we can substitute y = 0 into the equation and solve for x:
0 - 3 = (-3/4)x
-3 = (-3/4)x
To isolate x, we can multiply both sides of the equation by (-4/3):
(-4/3)(-3) = x
4 = x
Therefore, the x-intercept (x1, y1) of the line is (4, 0).
In summary, the point-slope form of the line is y - 3 = (-3/4)x, and the x-intercept is (4, 0).