Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept

Line MN passes through points M(4, 3) and N(7, 12). If the equation of the line is written in slope-intercept form, y = mx + b, what is the value of b? –15 –9 3 9

Related Posts

This Post Has 10 Comments

  1. b = -9.

    Step-by-step explanation:

    The line passes through (4, 3) and (7, 12). First, we need to find the slope: the rise over the run.

    (12 - 3) / (7 - 4) = 9 / 3 = 3.

    Now that we have the slope, we can say that m = 3. So, we have an equation of y = 3x + b. To find b, we can use M(4, 3) and say that y = 3 and x = 4.

    3 = 3 * 4 + b

    b + 12 = 3

    b = -9.

    Hope this helps!

  2. b=1

    Step-by-step explanation

    Vertical difference “y”

    Y2-Y1= 7-3=4

    Horizontal difference

    x2-x1=12-4=8

    Slope is =(y2-y1)/(x2-x1)

    M=4/8= 1/2

    3=1/2(4)+b

    3=2+b

    b=3-2

    B=1

  3. b = -9

    Step-by-step explanation:

    As we go from M(4, 3) to N(7, 12), x increases by 3 and y increases by 9.  Thus, the slope of the line segment connecting these two points is m = rise / run = m = 9/3, or just m = 3.

    Subbing the coordinates of M into y = mx + b, we get:

    3 = 3(4) + b, or 3 = 12 + b, so that b = -9.

  4. -9

    Step-by-step explanation:

    What b represents here is the y intercept.

    The first thing we will do here is to find the slope.

    Mathematically;

    m = (y2-y1)/(x2-x1)

    Plugging the values;

    m = (12-3)/(7-4) = 9/3 = 3

    The equation can thus be written as;

    y = 3x + b

    To get b, we can use any of the points since they lie on the line

    Let’s use point M

    Substitute the values of x and y in the equation

    3 = 3(4) + b

    3 = 12 + b

    b = 3-12 = -9

  5. For finding the value of b, we must consider that Line MN passes through points M(4, 3) and N(7, 12). With this condition y = mx + b, can be written 3=4m+ b (because line passes through M(4,3) ) and 12=7m+b, b ( because line passes through M(7,12)). We have a system of equation 4m+ b=3 7m+b=12 For solving this, 4m+b- (7m+b)= 3-12, it is equivalent to -3m= -9 and then m=3, if m=3 so 4x3 +b =3 implies b= 3 -12= -9, so the value of b= -9

Leave a Reply

Your email address will not be published. Required fields are marked *