114k views
1 vote
Write or type 3 linear equations in slope-intercept form whose graphs all pass through the point (-2, 5).

(Hints: There are infinitely many answers to this and your calculator can help you!)

User LudoMC
by
7.9k points

1 Answer

4 votes

Three linear equations in slope-intercept form that pass through (-2, 5) could be y = 2x + 9, y = -x + 3, and y = 0.5x + 6. Their slopes are chosen arbitrarily and demonstrate how the specified point affects the y-intercept of each line.

To write 3 linear equations in slope-intercept form that all pass through the point (-2, 5), we use the general format y = mx + b, where m is the slope and b is the y-intercept. The main answer in 2 lines is that any line with the slope m and passing through (-2, 5) can be given by plugging in the coordinates into y - y1 = m(x - x1) to find the y-intercept b and then rewriting as y = mx + b.

Choose different slopes (for example 2, -1, 0.5). Using one of these slopes, say 2, we will find the y-intercept by using the point-slope formula: 5 - 2(-2) = 5 + 4 = 9, so one line is y = 2x + 9. Similarly, for a slope of -1, the equation becomes 5 - (-1)(-2) = 5 - 2 = 3, leading to the line y = -x + 3. Lastly, using 0.5 as the slope, the y-intercept is calculated as 5 - 0.5(-2) = 5 + 1 = 6, resulting in y = 0.5x + 6.

these equations represent different lines that all intersect at the point (-2, 5), demonstrating how the slope influences the steepness and direction of the line, while the y-intercept determines where it crosses the y-axis.

User Chh
by
7.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories