Find a forula for the following function.
A line with slope 5 and x-intercept 10
is the answer y(x)= 5x-50
yes
y = m x + b
m = slope
b = y axis intercept
to get x axis intercept set y = 0
0 = m x + b
x = -b/m
here x = 50/5 = 10 sure enough
To find the equation of a line given its slope and x-intercept, you need to understand a few key concepts about linear equations.
First, the slope of a line (denoted as m) measures how steep or inclined the line is. It determines how much the y-coordinate changes for every unit increase in the x-coordinate. In this case, the slope is given as 5.
Second, the x-intercept is the point at which the line crosses the x-axis. In other words, it is the value of x when y is equal to zero. Given the x-intercept of 10, we know that the line intersects the x-axis at the point (10,0).
Now, to find the equation of a line, we can use the point-slope form of a linear equation. The formula is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope. To find the equation, we substitute the values we know into this formula.
In this case, we have:
x1 = 10 (the x-coordinate of the x-intercept)
y1 = 0 (the y-coordinate of the x-intercept)
m = 5 (the slope)
Substituting these values into the point-slope form, we get:
y - 0 = 5(x - 10)
Simplifying further, we have:
y = 5(x - 10)
Expanding the expression, we get:
y = 5x - 50
Therefore, the formula for the line with a slope of 5 and x-intercept of 10 is y = 5x - 50.