Question

Find an equation of the line that passes through the points (-2, 1) and (3, 3). Write your equation in either point-slope form, standard form, or slope-intercept form.

Answer 1

To find the equation of the line, calculate the slope (m), which is 2/5, using the two given points, then use the slope with one of the points to find the y-intercept (b=9/5). The equation of the line, in slope-intercept form, is y = (2/5)x + 9/5.

Step-by-step explanation:

To find an equation of the line that passes through the points (-2, 1) and (3, 3), we need to calculate the slope (m) of the line and use one of the points to write the equation in point-slope form, standard form, or slope-intercept form.

First, we find the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the given points, we get m = (3 - 1) / (3 - (-2)) = 2 / 5.

Now, using the slope-intercept form (y = mx + b) and one of the points, say (-2, 1), we can find the y-intercept (b). We substitute for x, y, and m to get: 1 = (2/5)(-2) + b, which simplifies to b = 1 + 4/5 = 9/5.

Finally, the equation of the line in slope-intercept form is y = (2/5)x + 9/5.

Answer 2

• (-2,1)
• (3,3)

m=3-1/3+2=2/5

Equation of line in point slope. form

`\\ \sf\longmapsto y-y_1=m(x-x_1)`

`\\ \sf\longmapsto y-1=2/5(x-(-2))`

`\\ \sf\longmapsto y-1=2/5(x+2)`

`\\ \sf\longmapsto 5y-5=2x+4`

`\\ \sf\longmapsto 2x-5y+9=0`