Slope and Intercept form || Equation of straight line
Criteria A: Knowing and Understanding
1. Rewrite each equation from slope-point form to slope-intercept form, y=mx+C and general form Ax+By+C=0.Criteria A: Knowing and Understanding
Maximum: 8
Objective:
i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations
ii. apply the selected mathematics successfully when solving problems
iii. solve problems correctly in a variety of contexts.
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a) y+3 = x – 5
b) y-6 = 4(x+1)
c) 𝑦−3= −12(𝑥+8)
2.Write an equation in slope-point form, y-y1=m(x-x1), of each line passing through the given point.
a) (12, -7) and (4, 5) b) (3, 4) and (4, 7)
3. Determine the equation of each line using slope-point form. Then, express each equation in slope-intercept form and in general form.
a) (5,2) and m=6 Slope-point form = ________________
General form = ___________________
b) (-8,3) and m=½ Slope-point form = ________________
General form = ___________________
4. Consider the line represented by 𝑦−1=23(𝑥−6) Identify the slope and a point on the line.
5. Write and equation in slope-point form, y-y1=m(x-x1), of the line passing through the given points.
a) (0, 9) and (2, 3) b) (-2, -3) and (-5, -7)
6. Use slope-point form to write an equation of a line through each pair of point. Express each equation in the form y=mx+c and in the form Ax+By+C=0.
a) (5,1) and (3,-7)
y=mx+c = ________________
Ax+By+C=0 = _____________
b) (4,5) and (2,6)
y=mx+c = ________________
Ax+By+C=0 = _____________
c) (5,-1) and (3,-4)
y=mx+c = ________________
Ax+By+C=0 = _____________
7. Consider the line passing through the points (-4,2) and (-2,6). What is the y-intercept of the line?
8. Rewrite the equation 4x – 2y = 12 in slope-intercept form.
9. A line passes through (0,1) and (3,7)
a) Using only slope-intercept form, y=mx+b, write the equation of the line.
b) Determine the equation of the line using only slope-point form.
10. Write the equation of each line using slope-point form. Then, convert to slope-intercept form.
a) Slope of 0 and through (4,5)
b) Same slope as 3x+y=5 and through (-2,4)
c) Same slope as the line x-2y+6=0 and the same x-intercept as the line 3x-2y=24
d) Same y-intercept as x+4y=8 and through (3,-4)
11. What is the equation of each line in slope-point form? Convert each equation to general form.
a) Slope of 3 and x-intercept of 4
b) Same slope as y=-4x+5 and through (2,-1)
c) Same x-intercept as the line3x+y=12 and through (0,2)
d) X-intercept of 2 and y-intercept of -6
12. What is the y-intercept of a line with a slope of ½ and an x-intercept of 4?
13. Determine the x-intercept of a line through (3,4) having a y-intercept of 2.