Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Get immediate and reliable solutions to your questions from a knowledgeable community of professionals on our platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Given the equation of the straight line AB is 3x+KY=8 where k is a constant. the straight line AB is parallel to the straight line connecting the point P(-1, 6) with the point Q(5, -3). Find the value of k then calculate the x-intercept of the straight line AB

Given The Equation Of The Straight Line AB Is 3xKY8 Where K Is A Constant The Straight Line AB Is Parallel To The Straight Line Connecting The Point P1 6 With T class=

Sagot :

If we have two parallel lines, than their slopes must be the same.

One way of comparing slopes of linear equations is to write them in the slope-intercept form:

[tex]y=mx+b[/tex]

In this form, m is the slope and b is the y-intercept.

So, let's write the first equation in this form:

[tex]\begin{gathered} 3x+ky=8 \\ ky=-3x+8 \\ y=-\frac{3}{k}x+\frac{8}{k} \end{gathered}[/tex]

To find the value of k, we can find the slope of the parallel line and compair it to the slope in this equation.

The slope of a line given two points on it can be calculated as:

[tex]m=\frac{y_2-y_1}{x_2-x_1}_{}[/tex]

Since we have points (-1, 6) and (5, -3), we can calculate the slope of the parallel line:

[tex]m=\frac{-3-6}{5-(-1)}=\frac{-9}{5+1}=-\frac{9}{6}=-\frac{3}{2}[/tex]

Since both lines are parallel, their slopes are the same.

We know that the slope of the first line is -3/k and the second line is -3/2, so, since they are parallel:

[tex]\begin{gathered} -\frac{3}{k}=-\frac{3}{2} \\ -3\cdot2=-3\cdot k \\ 2=k \\ k=2 \end{gathered}[/tex]

Since we have the value for k, we can substitute it into the equation for AB:

[tex]\begin{gathered} y=-\frac{3}{k}x+\frac{8}{k} \\ y=-\frac{3}{2}x+\frac{8}{2} \\ y=-\frac{3}{2}x+4 \end{gathered}[/tex]

To find the x-intercept, we can see that it happens when the value of y is equal to 0, so we can plug in y = 0 and find the value of x:

[tex]\begin{gathered} y=0 \\ 0=-\frac{3}{2}x+4 \\ \frac{3}{2}x=4 \\ x=\frac{2}{3}\cdot4 \\ x=\frac{8}{3} \end{gathered}[/tex]

So, the value of k is 2 and the x-intercept is 8/3.

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.