What is the equation of a line in slope intercept form that is parallel to y-4=2(x+3) that goes through (-1,2)
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Both problems are similar, so we can work the general case first.
For ax +by = c, you can solve for y to put the equation into slope-intercept form.
by = -ax +c . . . . . . subtract the x-term
y = (-a/b)x +c/b . .. divide by the coefficient of x
The slope is the x-coefficient, -a/b; the y-intercept is c/b. The function is an odd-degree polynomial function, so its domain and range are both "all real numbers."
2x+3y=18
Slope-intercept form: y = (-2/3)x +6
Domain: all real numbers
Range: all real numbers
Slope: -2/3
Y-intercept: 6
3x-4y > 16
Slope-intercept form: y < (3/4)x -4
Domain: all real numbers
Range: all real numbers
Slope: 3/4
Y-intercept: -4
_____
You will note that the inequality symbol in y < (3/4)x -4 is reversed from that in 3x -4y > 16. That is because in solving for y, we divided by -4. When you multiply or divide an inequality by a negative number, you must reverse the sense of the inequality.
For ax +by = c, you can solve for y to put the equation into slope-intercept form.
by = -ax +c . . . . . . subtract the x-term
y = (-a/b)x +c/b . .. divide by the coefficient of x
The slope is the x-coefficient, -a/b; the y-intercept is c/b. The function is an odd-degree polynomial function, so its domain and range are both "all real numbers."
2x+3y=18
Slope-intercept form: y = (-2/3)x +6
Domain: all real numbers
Range: all real numbers
Slope: -2/3
Y-intercept: 6
3x-4y > 16
Slope-intercept form: y < (3/4)x -4
Domain: all real numbers
Range: all real numbers
Slope: 3/4
Y-intercept: -4
_____
You will note that the inequality symbol in y < (3/4)x -4 is reversed from that in 3x -4y > 16. That is because in solving for y, we divided by -4. When you multiply or divide an inequality by a negative number, you must reverse the sense of the inequality.