a line passes through (1, 8) and is perpendicular to the graph y = 2x+1. what equation represents the line in slope-intercept form?
First, determine the slope of the given equation y = 2x + 1. The slope-intercept form of a line is y = mx + b, where m is the slope. In this case, the slope is 2.
To find the slope of a line perpendicular to this, take the negative reciprocal of the slope. The negative reciprocal of 2 is -1/2.
Now we have the slope for the new line. To find the equation in slope-intercept form, we need to use the point-slope form of a line: y - y1 = m(x - x1). We can use the point (1, 8) and the slope -1/2 for this.
Plugging in the values, we get:
y - 8 = (-1/2)(x - 1)
Now, simplify and rearrange this equation into slope-intercept form:
y - 8 = (-1/2)(x) + (1/2)
y - 8 = (-1/2)x + 1/2
y = (-1/2)x + (1/2) + 8
y = (-1/2)x + 17/2
Thus, the equation represents the line in slope-intercept form is y = (-1/2)x + 17/2.