Find the x and y intercepts of a line that is perpendicular to the line y = -9/8x + 1 and passes through the point (18, -8).

perpendicular means the slope is the negative reciprocal...

y= 8/9 x + b is the general form, put in the point 18.-8, and solve for b, and you have the equation.
Put in x=0, and you have the y intercept.
Put in y=0, and you have the x intercept.

To find the x and y intercepts of a line perpendicular to the given line, we need to determine the equation of the perpendicular line first.

The given line equation is y = -9/8x + 1, which is in slope-intercept form (y = mx + b) where m is the slope and b is the y-intercept.

Since we want a perpendicular line, its slope will be the negative reciprocal of the given line.

The slope of the given line is -9/8, so the slope of the perpendicular line will be the negative reciprocal, which is 8/9.

Now, we have the slope of the perpendicular line (8/9) and a point it passes through (18, -8).

Using the point-slope form of a linear equation (y - y1 = m(x-x1)), we can substitute the values to find the equation of the perpendicular line:

y - (-8) = (8/9)(x - 18)

Simplifying the equation:

y + 8 = (8/9)x - 16/9

To find the x-intercept, we set y to zero and solve for x:

0 + 8 = (8/9)x - 16/9

16/9 = (8/9)x

x = (9/8)*(16/9)

x = 2

Therefore, the x-intercept is 2.

To find the y-intercept, we set x to zero and solve for y:

y + 8 = (8/9)(0 - 18)

y + 8 = (-16/9)(18)

y + 8 = -32/3

y = -32/3 - 8

y = -32/3 - 24/3

y = -56/3

Therefore, the y-intercept is -56/3.

The x-intercept is 2, and the y-intercept is -56/3.

To find the x and y intercepts of a line that is perpendicular to another line, we need to understand the relationship between the slopes of the two lines.

The given line is y = -9/8x + 1. Let's determine its slope. The equation is in the standard slope-intercept form, y = mx + b, where m is the slope. By comparing this equation to the given equation, we can determine that the slope of the given line is -9/8.

To find the slope of a line perpendicular to another line, we need to take the negative reciprocal of the given slope. The negative reciprocal of -9/8 is 8/9.

Now that we have the slope of the perpendicular line, we can proceed to find the equation of the line using the point-slope form. The point-slope form of a line is given by y - y1 = m(x - x1), where (x1, y1) is a point on the line, and m is the slope.

Plugging in the values we have, the equation of the line is:

y - (-8) = 8/9(x - 18)

Simplifying this equation gives:

y + 8 = 8/9(x - 18)

Next, we can manipulate this equation into the slope-intercept form, y = mx + b:

y + 8 = 8/9x - 16/9

Subtracting 8 from both sides:

y = 8/9x - 144/9 - 8/9

Simplifying further:

y = 8/9x - 152/9

Now we have the equation of the line perpendicular to the given line. To find the x-intercept, we set y to zero, because the x-intercept is the point where the line crosses the x-axis.

0 = 8/9x - 152/9

Adding 152/9 to both sides:

152/9 = 8/9x

Simplifying:

x = (152/9) / (8/9)

Dividing the numerators and denominators:

x = (152/8)

Simplifying further:

x = 19

So, the x-intercept is 19.

To find the y-intercept, we set x to zero, because the y-intercept is the point where the line crosses the y-axis.

y = 8/9(0) - 152/9

Simplifying:

y = -152/9

So, the y-intercept is -152/9.

In summary, the line that is perpendicular to y = -9/8x + 1 and passes through the point (18, -8) has an x-intercept of 19 and a y-intercept of -152/9.