Question

Graph the line with the given point and slope.
Through ​(1​,1​); slope= -4/5

Answer 1

To graph the line with the given point (1,1) and slope -4/5, we can use the point-slope form of a linear equation:

y - y₁ = m(x - x₁)

where (x₁, y₁) is the given point and m is the slope.

Plugging in the values, we have:

y - 1 = (-4/5)(x - 1)

Now, let's rearrange the equation into slope-intercept form (y = mx + b), where b is the y-intercept:

y - 1 = (-4/5)x + 4/5

Simplifying further:

y = (-4/5)x + 4/5 + 1
y = (-4/5)x + 4/5 + 5/5
y = (-4/5)x + 9/5

Now we have the equation of the line in slope-intercept form. To graph it, plot the given point (1,1) and use the slope to find additional points. The slope is -4/5, which means for every 5 units you move to the right, you will move 4 units downward.

Using this information, we can plot the point (1,1) and find additional points by moving 5 units to the right and 4 units down from the previous point.

Using (1,1) as the starting point:
(1, 1)
(6, -3)
(11, -7)
(16, -11)

Connect the points, and you will have the graph of the line.