Final answer:
The equation of the line with a slope of – 2/5 that passes through the point (17, – 6) is y = – 2/5x + 4/5 when written in slope-intercept form (y = mx + b).
Step-by-step explanation:
To write the equation of a line in slope-intercept form you need to know the slope of the line and the y-intercept. The slope-intercept form is given by the equation y = mx + b where m is the slope and b is the y-intercept. For the given line with a slope of – 2/5 that passes through the point (17, – 6), we can substitute the values into the point-slope form of a line equation which is y – y1 = m(x – x1) and then rearrange it to slope-intercept form.
Starting with the point-slope form:
y – (–6) = (– 2/5)(x – 17)
Now, we simplify and solve for y to get it into slope-intercept form:
y + 6 = – 2/5x + 34/5y = – 2/5x + 34/5 – 30/5y = – 2/5x + 4/5
So the equation of the line in slope-intercept form is y = – 2/5x + 4/5.