Algebra 1 help please

Question

I have to write an equation for each condition listed...

 

1. The line with a slop of -8 and a y-intercept of 3 (in slope-intercept form)

 

2. The line that passes through (-2, 0) and has a slope of 5 (in point-slope form)

 

3. The horizontal line that passes through (-2, 6)

 

4. The vertical line that passes through (-2, 6) 

Answer 1

Memorize your repertoire of equations for straight line functions!

 

SLOPE INTERCEPT:  y = mx + b

 

POINT-SLOPE:         y - y_o = m(x - x_o)

 

VERTICAL LINE:       x = constant    ⇐ note: NOT a function!

 

HORIZONTAL LINE:  y = constant

 

Also, the general form:  Ax + By = C.  If the equation comes in this form, you can put into slope intercept form by "solving for y."

 

Every studenbt must learn, with understanding, these basic facts, AND THEY WILL BE USED AGAIN AND AGAIN THROUGHOUT YOUR ACADEMIC YEARS (and beyond, if you have kids and/or grandchildren).

 

So take the given data in your specific problems and apply these equations, after you substitute the given data in the right places (m = slope, b = y-intercept, etc.).

Answer 2

1. Slope-intercept form is y = mx + b where m is the slope and b is the y-intercept. From the given information we know m = -8 and b = 3. Replace the letters in the equation with the numbers to get y = -8x + b.

 

2. Point-slope form is y - y1 = m(x - x1) where m is the slope, y1 is the y value of the point, and x1 is the x value of the point. From the given information we know m = 5, y1 = 0, and x1 = -2. Again replace the letters in the equation with the numbers to get y - 0 = 5(x - -2). This can be simplified to y = 5(x + 2) or y = 5x + 10.

 

3. A horizontal line is always in the form of y = y1 where y1 is the y value of the point given (note: this is because the slope is equal to zero, the y values do not change along the line). We know that y1 = 6 from the problem, so the equation becomes y = 6.

 

4. A vertical line is always in the form of x = x1 where x1 is the x value of the point given (note: this is because the slope is not defined, the x values do not change along the line). We know that x1 = -2 from the problem, so the equation becomes x = -2.